He has sprinkled America with the bright red Os of Mobil gas stations, filled the skies with the radiant lines of Pan Am's blue globe, and brought the rainbow feathers of NBC's peacock into millions of living rooms across the US. But Ivan Chermayeff, the 82-year-old designer behind some of the world's most memorable logos, feels most at home surrounded by junk, with a big pair of scissors in his hand. "I really like cutting and slicing and tearing," he says, eyes lighting up at the thought. "I have lots of pairs of scissors of all different sizes, that cut in all different ways. And I have boxes and boxes of trash – I just can't stop picking up garbage."

The results of these two obsessions are now on show in an exhibition of his collages and prints at the De La Warr pavilion in Bexhill, the sparkling 1930s vision of modernity parked like a continental cruise liner on the south coast of England. The show, Cut and Paste, is something of a family affair: the building was designed in 1935 by Ivan's Russian emigre father, Serge, together with German architect Erich Mendelsohn, and the exhibition has been designed by his architect son Sam, fresh from minimalist Japanese practice Sanaa. Together in the same space, the three generations of Chermayeffs show that a keen graphic eye runs in the family.

Covering over 60 years of cutting and pasting, the show focuses on Chermayeff's personal artwork, revealing the ad-hoc, rough and ready process behind the years of crisply polished branding produced by his office, Chermayeff & Geismar & Haviv. There are crumpled envelopes and crushed tin cans, scraps of billboards and torn newsprint, all assembled with elegant brevity to form strange animals and faces, abstract forms that trigger dreamy associations.

A crumpled glove dotted with a few pebbles becomes a startled thief, caught in the act. And who knew that a child's wooden shoe last, when stuck on a scrap of blue paper in the shape of a leaping body, looks just like the face of an ecstatic runner? Or that flattened tin cans, driven over by countless trucks, can be as beautiful and unique as snowflakes? All have been scavenged by the magpie Chermayeff and reborn in startling new forms.

"It's important not to think too hard," he says. "Most of these collages appeared in about 15 seconds – but I might have some of these scraps lying about for years before they find their right home." It's something he does while waiting for a phone call, or in between meetings, momentarily distracted, allowing his mind to wander and make unexpected connections.

These games of free association have always fed into his work for commercial clients, displayed here in a series of posters for Mobil-sponsored TV dramas. One of the most famous, produced in 1983, simply depicts a homburg hat and a smouldering cigar, from which emerges a scribbled cloud of smoke, the face obscured behind a foggy haze. It is an apt image for Winston Churchill: The Wilderness Years, evoking its subject in less time than it takes to read the title. "The goal is always to make something simple and memorable," says the designer, who was born in London in 1932 but moved to the US eight years later. "You must be as clear and direct as possible." The red O of Mobil was designed, he says, "to whip out at you down the highway before you can even read the sign."

'I was always putzing about with garbage' … Chermayeff. PR

The combination of clarity and wit made Chermayeff a favourite illustrator for newspapers and magazines. For a 1960 cover of Harper's magazine, he took the headline The Missile Mess, and simply fired the two dots of each letter "i" up the page. When the twin towers collapsed, he was approached to illustrate the New York Times's op-ed. He took the letters U and S and ripped off the uprights of the U, leaving two raw stumps: a brutally simple image of a country torn apart.

Chermayeff's love of using found objects began when he was at school, intimidated by the skills of his fellow students. "They could all draw and paint a lot better than I could," he says, "so I developed a real fear of drawing. I was always putzing around with garbage at home, but whatever I made, my father would say it was great. He really encouraged me."

Seven decades on, he is still an ardent bricoleur and shows no sign of slowing down. His fingers are still fidgeting, his eyes still roaming, spotting accidental beauty in the detritus of everyday life. "I just can't sit still," he says. "And there's still a lot of trash to get through."

• Ivan Chermayeff: Cut and Paste, is at the De La Warr Pavilion, Bexhill-on-Sea, until 14 September. Details: dlwp.com